Dissertation: Mason's remarks

dissertation/TDA.bib

@@ -819,4 +819,58 @@ novel application of the discriminatory power of {PIs}.},
 	date = {2010},
 	doi = {10.1214/10-IMSCOLL609},
 	file = {Full Text PDF:/home/dimitri/Zotero/storage/N8UHEK9G/Adler et al. - 2010 - Persistent homology for random fields and complexe.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/29PXN97Q/1288099016.html:text/html}
+}
+
+@article{cohen-steiner_stability_2007,
+	title = {Stability of Persistence Diagrams},
+	volume = {37},
+	issn = {0179-5376, 1432-0444},
+	url = {https://link.springer.com/article/10.1007/s00454-006-1276-5},
+	doi = {10.1007/s00454-006-1276-5},
+	abstract = {The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.},
+	pages = {103--120},
+	number = {1},
+	journaltitle = {Discrete \& Computational Geometry},
+	shortjournal = {Discrete Comput Geom},
+	author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John},
+	urldate = {2018-07-31},
+	date = {2007-01-01},
+	langid = {english},
+	file = {Full Text PDF:/home/dimitri/Zotero/storage/4WEUZ4B5/Cohen-Steiner et al. - 2007 - Stability of Persistence Diagrams.pdf:application/pdf;Snapshot:/home/dimitri/Zotero/storage/5P323WWZ/s00454-006-1276-5.html:text/html}
+}
+
+@article{chazal_persistence_2014,
+	title = {Persistence stability for geometric complexes},
+	volume = {173},
+	issn = {0046-5755, 1572-9168},
+	url = {https://link.springer.com/article/10.1007/s10711-013-9937-z},
+	doi = {10.1007/s10711-013-9937-z},
+	abstract = {In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, Čech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and Čech complexes built on top of compact spaces.},
+	pages = {193--214},
+	number = {1},
+	journaltitle = {Geometriae Dedicata},
+	shortjournal = {Geom Dedicata},
+	author = {Chazal, Frédéric and Silva, Vin de and Oudot, Steve},
+	urldate = {2018-07-31},
+	date = {2014-12-01},
+	langid = {english},
+	file = {Snapshot:/home/dimitri/Zotero/storage/7EESRFL3/s10711-013-9937-z.html:text/html}
+}
+
+@inproceedings{zomorodian_tidy_2010,
+	location = {New York, {NY}, {USA}},
+	title = {The Tidy Set: A Minimal Simplicial Set for Computing Homology of Clique Complexes},
+	isbn = {978-1-4503-0016-2},
+	url = {http://doi.acm.org/10.1145/1810959.1811004},
+	doi = {10.1145/1810959.1811004},
+	series = {{SoCG} '10},
+	shorttitle = {The Tidy Set},
+	abstract = {We introduce the tidy set, a minimal simplicial set that captures the topology of a simplicial complex. The tidy set is particularly effective for computing the homology of clique complexes. This family of complexes include the Vietoris-Rips complex and the weak witness complex, methods that are popular in topological data analysis. The key feature of our approach is that it skips constructing the clique complex. We give algorithms for constructing tidy sets, implement them, and present experiments. Our preliminary results show that tidy sets are orders of magnitude smaller than clique complexes, giving us a homology engine with small memory requirements.},
+	pages = {257--266},
+	booktitle = {Proceedings of the Twenty-sixth Annual Symposium on Computational Geometry},
+	publisher = {{ACM}},
+	author = {Zomorodian, Afra},
+	urldate = {2018-07-31},
+	date = {2010},
+	keywords = {computational topology, simplicial set, vietoris-rips complex, witness complex}
 }